Image and video processing are forms of signal processing. Signal processing allows a set of characteristics or parameters related to the image or video to be obtained. Signal processing including analog signal processing, discrete time signal processing, and digital signal processing, which may involve a one-dimensional (“1D”), two-dimensional (“2D”) or three-dimensional (“3D”) input signal to which signal processing techniques are applied.
Signal processing techniques include transform-based processing such as discrete or integral transforms which were implemented prior to AM-FM processing. As an example, a 1D analysis of transform-based processing includes the use of short-time Fourier Transform (“STFT”) for non-stationary signals. When using STFT, the fast Fourier Transform (“FFT”) of different time intervals of the signals is used to determine the frequency and phase content. Thus, the STFT is a convenient 2D representation that provides frequency content information at different time intervals. A disadvantage is that the STFT cannot be effectively generalized to images and videos. For example, using STFT for images would produce a four-dimensional (“4D”) representation and using STFT for video would produce a six-dimensional (“6D”) representation.
The discrete Wavelet Transform (“DWT”) has also been used for transform-based image processing. Unlike Fourier Transforms, Wavelet Transforms are based on specific functions defined at different scales and durations. Thus, the DWT is a space-frequency representation of the input signal and it is related to harmonic analysis is as in Fourier Transform. While FFT uses equally spaced frequency division, DWT uses logarithmic divisions of the frequency. A disadvantage is that DWT does not measure frequency content directly.
The development of accurate methods for estimating amplitude-modulation frequency-modulation image decompositions is of great interest due to is potentially significant impact on image analysis applications including in the areas of signal, image and video processing. Applications in signal processing include speech signal analysis. Image processing applications include shape from shading, image pattern analysis, image interpolation, fingerprint classification, image retrieval in digital libraries, image segmentation, and damaged image texture repairs. Applications in video processing include cardiac image segmentation, motion estimation, and motion reconstruction, to name a few.
A number of techniques exist to reconstruct an image from its AM-FM representation in terms of amplitude, phase and frequency functions. Reconstruction of an image involves estimating or computing the amplitude, phase and frequency components of the signals emerging from each filter channel and using these components to create an AM-FM representation that best approximate the original image signal. Generally, the more components and channels used, the more information is recovered, the better the image signal is restored and the better the image is regenerated. If every component of every channel is used, this will yield to the best reconstruction of the original image. However, such approaches lead to very redundant representations that can lead to very inefficient applications in image analysis. Thus, the goal of an efficient reconstruction process is select few channels and components that best approximates the image signal.
The AM-FM Dominant Component Analysis (“DCA”) and Channelized Component Analysis (“CCA”) are methods used that consist of applying a filterbank to the Hilbert-transformed image, and then applying AM-FM demodulation of each bandpass filtered image. Using DCA, every pixel delivers estimated modulating functions corresponding to the AM-FM component that is locally dominant at that pixel. Using CCA, a filterbank partitions the image into components on a spatially global basis. Each resulting AM-FM component is restricted to lie in a single channel over the entire image domain. With CCA, the number of components in the computed image model is necessarily equal to the number of channels in the filterbank. AM-FM reconstructions based on the CCA use a reasonably small number of locally coherent components. In contrast, those based on the DCA only use one component—the estimates from the channel with the maximum amplitude estimate. A disadvantage of DCA and CCA are that they are known to produce noticeable visual artifacts.
Optimizing the quality of an AM-FM reconstruction image is important due to the potentially significant impact on various applications. Thus, there is demand for high quality reconstructions in both stationary and non-stationary processing for use in a variety of contexts and applications. The present invention satisfies this demand.